{
  "annotation_id": "fb8eb1d3-c282-44e5-b3a6-88e77014653d",
  "date_created": "2026-03-02T18:01:38.620000Z",
  "date_modified": "2026-03-02T18:01:38.620000Z",
  "file_hash": "799eef48e34f3b81de468473f3b5f81befdb9336d64827000aa99152f5644aa2",
  "private": false,
  "record": {
    "abstract": "A stochastic process with self-interaction as a model of quantum field theory\nis studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with\ninteraction of the form x^{(\\alpha)}(t)^4, where $\\alpha$ indicates the\nfractional derivative. Using Bogoliubov\u0027s R-operation we investigate\nultraviolet divergencies for the various parameters $\\alpha$. Ultraviolet\nproperties of this one-dimensional model in the case $\\alpha=3/4$ are similar\nto those in the $\\phi^4_4$ theory but there are extra counterterms. It is shown\nthat the model is two-loops renormalizable. For $5/8\\leq \\alpha \u003c 3/4$ the\nmodel has a finite number of divergent Feynman diagrams. In the case\n$\\alpha=2/3$ the model is similar to the $\\phi^4_3$ theory. If $0 \\leq \\alpha \u003c\n5/8$ then the model does not have ultraviolet divergencies at all. Finally if\n$\\alpha \u003e 3/4$ then the model is nonrenormalizable. This model can be used for\na non-perturbative study of ultraviolet divergencies in quantum field theory\nand also in theory of phase transitions.",
    "arxiv_id": "quant-ph/0008063",
    "authors": [
      "Yaroslav Volovich"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1142/9789812810809_0027",
    "title": "Interacting Stochastic Process and Renormalization Theory",
    "url": "https://arxiv.org/abs/quant-ph/0008063"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "62eae81a-b160-4d4b-acfe-c30891625e56",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}